A non-linear mixed effect model for innate immune response ...uu.diva-portal.org/smash/get/diva2:1295338/FULLTEXT01.pdf · The recognition of ETX through toll-like receptor 4 (TLR-4)

RESEARCH ARTICLE

A non-linear mixed effect model for innate

immune response: In vivo kinetics of

endotoxin and its induction of the cytokines

tumor necrosis factor alpha and interleukin-6

Anders ThorstedID1*, Salim Bouchene1, Eva Tano2, Markus CastegrenID

3,4,5,

Miklos LipcseyID6, Jan Sjolin3, Mats O. Karlsson1, Lena E. Friberg1, Elisabet I. NielsenID

1

1 Pharmacometrics Research Group, Department of Pharmaceutical Biosciences, Uppsala University, Uppsala,

Sweden, 2 Section of Clinical Microbiology and Infectious Medicine, Department of Medical Sciences, Uppsala

University Hospital, Uppsala, Sweden, 3 Section of Infectious Diseases, Department of Medical Sciences,

Uppsala University Hospital, Uppsala, Sweden, 4 Division of Perioperative Medicine and Intensive Care,

Karolinska University Hospital, Stockholm, Sweden, 5 Department of Clinical Science, Intervention and

Technology, Karolinska Institute, Stockholm, Sweden, 6 Hedenstierna Laboratory, Section of Anesthesiology

and Intensive Care, Department of Surgical Sciences, Uppsala University Hospital, Uppsala, Sweden

* [email protected]

Abstract

Endotoxin, a component of the outer membrane of Gram-negative bacteria, has been exten-

sively studied as a stimulator of the innate immune response. However, the temporal

aspects and exposure-response relationship of endotoxin and resulting cytokine induction

and tolerance development is less well defined. The aim of this work was to establish an in

silico model that simultaneously captures and connects the in vivo time-courses of endo-

toxin, tumor necrosis factor alpha (TNF-α), interleukin-6 (IL-6), and associated tolerance

development. Data from six studies of porcine endotoxemia in anesthetized piglets (n =

116) were combined and used in the analysis, with purified endotoxin (Escherichia coli

O111:B4) being infused intravenously for 1–30 h in rates of 0.063–16.0 μg/kg/h across stud-

ies. All data were modelled simultaneously by means of importance sampling in the non-lin-

ear mixed effects modelling software NONMEM. The infused endotoxin followed one-

compartment disposition and non-linear elimination, and stimulated the production of TNF-αto describe the rapid increase in plasma concentration. Tolerance development, observed

as declining TNF-α concentration with continued infusion of endotoxin, was also driven by

endotoxin as a concentration-dependent increase in the potency parameter related to TNF-

α production (EC50). Production of IL-6 was stimulated by both endotoxin and TNF-α, and

four consecutive transit compartments described delayed increase in plasma IL-6. A model

which simultaneously account for the time-courses of endotoxin and two immune response

markers, the cytokines TNF-α and IL-6, as well as the development of endotoxin tolerance,

was successfully established. This model-based approach is unique in its description of the

time-courses and their interrelation and may be applied within research on immune

response to bacterial endotoxin, or in pre-clinical pharmaceutical research when dealing

with study design or translational aspects.

PLOS ONE | https://doi.org/10.1371/journal.pone.0211981 February 21, 2019 1 / 18

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OPEN ACCESS

Citation: Thorsted A, Bouchene S, Tano E,

Castegren M, Lipcsey M, Sjolin J, et al. (2019) A

non-linear mixed effect model for innate immune

response: In vivo kinetics of endotoxin and its

induction of the cytokines tumor necrosis factor

alpha and interleukin-6. PLoS ONE 14(2):

e0211981. https://doi.org/10.1371/journal.

pone.0211981

Editor: Johnson Rajasingh, University of Kansas

Medical Center, UNITED STATES

Received: October 16, 2018

Accepted: January 24, 2019

Published: February 21, 2019

Copyright: © 2019 Thorsted et al. This is an open

access article distributed under the terms of the

Creative Commons Attribution License, which

permits unrestricted use, distribution, and

reproduction in any medium, provided the original

author and source are credited.

Data Availability Statement: All relevant data are

within the manuscript and its Supporting

Information files.

Funding: This project was sponsored by the

Swedish Foundation for Strategic Research (SSF,

https://strategiska.se/). The funders had no role in

study design, data collection and analysis, decision

to publish, or preparation of the manuscript.

http://orcid.org/0000-0003-1804-2703

http://orcid.org/0000-0002-9292-0298

http://orcid.org/0000-0002-1976-4129

http://orcid.org/0000-0003-0725-214X

https://doi.org/10.1371/journal.pone.0211981

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http://creativecommons.org/licenses/by/4.0/

https://strategiska.se/

Introduction

Bacterial infection will invoke the host immune system and elicit a response of varying magni-

tude and duration depending on factors relating to the host and/or the invading pathogen.

The prototypical pathogen-associated molecular pattern (PAMP) from Gram-negative bacte-

ria is endotoxin (ETX), also called lipopolysaccharide, located in the outer membrane [1, 2].

Though ETX exhibits no toxicity per se, recognition by the immune system lead to a response

aimed at clearing the pathogen to protect the host. However, an aggravated response can lead

to tissue and organ injury, a clinical condition known as sepsis, defined as life-threatening

organ dysfunction caused by a dysregulated host response to infection [3]. Sepsis is associated

with high mortality rates and high per-patient costs of treatment in the intensive care unit and

constitute a serious health care problem [4, 5].

The recognition of ETX through toll-like receptor 4 (TLR-4) on immune cells (e.g. tissue

resident macrophages) will lead to a predominantly pro-inflammatory innate immune

response involving the release of a plethora of cytokines in addition to activation and tissue

infiltration of white blood cells [6–8]. Cytokines are endogenous mediators involved in a com-

plex network of secondary reactions and cell-signalling, such as stimulation of acute phase pro-

tein secretion by the liver or activation of lymphocytes and thrombocytes [9]. Two key

cytokines of innate immunity are tumor necrosis factor alpha (TNF-α) and interleukin-6 (IL-

6) whose plasma concentration quickly increase over baseline values upon exposure to ETX,

making them interesting biomarkers for the extent of early immune activation in a research

setting [10].

While the in vitro and in vivo immune response to ETX is thoroughly investigated, a knowl-

edge gap exists concerning the time-courses in the interplay between bacteria (or bacterial

products) and host-response. Mathematical modelling is a key tool in the understanding of

time-courses, and multiple models describing immune response to different infections are

available. However, many of these are higly complex (alleviated by fixing certain parameters to

literature values) [11, 12], discrete in nature and not able to describe time-courses [13], or not

generalized for a population [14]. As alternative, a non-linear mixed effects modelling

approach offers a simultaneous description of the typical tendency of data as well as consider-

ation of the individual variability in a population, based on a set of ordinary differential equa-

tions. As such, data from multiple studies and individuals can be combined in the same model,

and simulations of the system and its variability can be carried out according to different

designs [15].

A wide range of pharmacokinetic-pharmacodynamic (PKPD) models have been developed

to describe and understand the effects of antibiotics on bacteria [16]. These models are ac-

companied by a comprehensive collection of population PK models describing the time-

course of antibiotics in different patient populations. However, the impact of the host im-

mune system on the clearance of an infection, and the impact of the immune system on the

physiological functioning of the host is usually disregarded. Development of models that

describes the temporal aspects of immune activation is needed prior to a simultaneous integra-

tion of antibiotic and immune effects on a given pathogen, something that would be of value

when selecting an appropriate antibiotic treatment regimen for optimizing therapy in patients

[17].

In this work, we developed a mathematical model that simultaneously account for and con-

nect the in vivo time-courses and interrelation of ETX, TNF-α and IL-6, and associated toler-

ance development, based on data from a large cohort of endotoxemic piglets.

Modelling endotoxin exposure and innate cytokine response


Competing interests: The authors have declared

that no competing interests exist.


Results

The studies presented in Table 1 formed the basis for the development of our integrated

model (see respective reference for a thorough description), with one study (G) held out and

used for external evaluation as it was only made available after the modelling work had been

initiated. The dataset consisted of 116 individuals and 2391 observations (278 ETX, 1068 TNF-

α, and 1045 IL-6) and led to the final model structure presented in Fig 1, with maximum likeli-

hood estimates and variances as presented in Table 2 (see Methods). The final dataset used

during model development, as well as code describing the final model structure is included as

supplementary information (S1 Table and S1 Text). Each sub-model is explained in detail in

the following sections. In summary, ETX kinetics followed one-compartment disposition and

saturable elimination, and the concentration-time course stimulated the production rate of

Table 1. Overview of the studies used for model building (A-F) and external evaluation (G), including a short description of the design, number of animals, study

length, infusion rates, assays and the amount of data points available for each modelled outcome.

Study Short Description of the Design N Study

Length

ETX

Batch

(EU/

μg)

Infusion Rates

(μg/kg/h)

Data Samples

(BLOQ)

Assay a (LOQ) Reference

A Twenty-four hour intravenous infusion of ETX at low

rates, followed by six hour intravenous infusion of ETX at

much higher rates to understand the development of ETX

tolerance, including a control group with intravenous

infusion of saline.

27 30 h 1000 Pre-exposure: 0;

0.063; 0.250

TNF-

α439 (0) DuoSet (NA) [18]

IL-6 422 (0) DuoSet (NA)

ETX-challenge: 0;

1.0; 4.0

B Twenty-four hour intravenous infusion of ETX at low

rates with ex vivo stimulation to assess the development of

ETX tolerance, including a control group with

intravenous infusion of saline.

21 24 h 1000 0; 0.063; 0.250 TNF-

α186 (0) DuoSet (NA) [19]

IL-6 176 (0) DuoSet (NA)

C Six hour intravenous infusion of ETX to examine the dose

(-exposure)-response relationship of ETX, including a

control group with intravenous infusion of saline.

20 6 h 3000 0; 0.063; 0.250;

1.0; 4.0; 8.0; 16

ETX 75 (0) Endochrome (NA) [20]

TNF-

α132 (77) BioSource (10)

IL-6 132 (34) Quantikine (10)

D Three hour intravenous infusion of ETX, with

accelerating or decelerating rates for each hour, in order

to examine the impact of infusion rate on immune

response and ETX tolerance.

18 6 h 3000 Accelerating:

0.063; 1.0; 4.0

TNF-

α117 (0) BioSource (NA) [21]


Decelerating: 4.0;

1.0; 0.063

E One, two or three hour intravenous infusion of ETX at

two different infusion rates, to mimic removal of ETX,

including a control group with infusion of saline.

26 6 h 1000 0; 0.063; 4.0 ETX 178 (0) Endochrome (NA) [22]

TNF-

α175 (79) DuoSet (60)

IL-6 178 (41) DuoSet (60)

F Six hour intravenous infusion of ETX, starting at a higher

infusion rate during the first thirty minutes.

4 6 h 3000 1.0; 4.0 ETX 28 (0) Coatest (NA) [23]

TNF-

α28 (13) BioSource (10)


G Six hour intravenous infusion of ETX at a constant rate 6 6h 3000 0.5 TNF-

α42 (10) DuoSet (NA) [24]

IL-6 42 (0) DuoSet (200)

Abbreviations: BLOQ: below limit of quantification; ETX: endotoxin; EU: endotoxin units; IL-6: interleukin-6; LOQ: limit of quantification; N: number; NA: not

applicable; TNF-α: tumor necrosis factor alphaa Duoset: D686 (TNF-α) and DY690 (IL-6), R&D Systems, Minneapolis, MN, USA. Endochrome: Endochrome-K, Charles River Endosafe, Charleston, SC, USA.

BioSource: KSC3011/KSC3012, Biosource International, Nivelles, Belgium. Quantikine: P6000, R&D Systems, Minneapolis, MN, USA. Coatest: Coatest Plasma

Chromo-LAL, Charles River Endosafe, Charleston, SC, USA.

https://doi.org/10.1371/journal.pone.0211981.t001





TNF-α through a sigmoidal Emax relationship. Simultaneously, the ETX concentration-time

course was responsible for a delayed increase in the potency parameter of the ETX-TNF-αrelationship, thereby introducing tolerance of varying magnitude dependent on prior ETX

exposure. The concentration-time courses of ETX and TNF-α simultaneously increased the

production rate of IL-6, with appearance in plasma delayed through a chain of transit

compartments.

Infused endotoxin

The infused ETX was distributed according to a one-compartmental model, with elimination

described as a non-linear relationship to concentration, and a constant assay-dependent base-

line (BASEETX) added to the ETX predictions. Addition of a peripheral compartment was not

significant according to the statistical measure of model fit (change in objective function value,

ΔOFV = -4.29 vs. one-compartment), but the non-linear elimination resulted in an improved fit

(ΔOFV = -12.9 vs. linear). Terms describing inter-individual variability (IIV) was supported for

the parameters KM, VC and BASEETX, with a negative correlation between KM and VC (-0.42).

An indication of contamination was observed in early samples for a proportion of the pig-

lets, with ETX concentrations higher than the modelled constant ETX baseline (most obvious

in control and low-dose groups shown in Fig 2). This was handled by implementing a mixture

model describing two sub-populations. The central compartment for sub-population one was

initialized to zero, whereas it was initialized to a quantity directly proportional to BASEETX,i

for sub-population two, as described by:

AETX;i;t¼0 ¼ BASEETX;i � Propcont ð1Þ

This initial amount was allowed to decay over time together with the infused ETX, and

Fig 1. Schematic of the final model structure, linking the endotoxin concentration-time course (CETX) to induction of tumor

necrosis factor alpha (CTNF-α) through a sigmoidal Emax relationship, and to development of tolerance (EC50) through an Emax

relationship. Both time-courses stimulate the induction of interleukin-6 (CIL-6) with linear relationships to endotoxin and tumor

necrosis factor alpha. For parameter description and estimates, see Table 2.

https://doi.org/10.1371/journal.pone.0211981.g001





significantly improved the fit (ΔOFV = -80.8), the residual and simulation based diagnostics,

and decreased the residual unexplained variability (RUV).

Host response: TNF-α and IL-6

The relationship between ETX exposure, a potent TLR-4 agonist, and host response measured

by TNF-α was initially established by letting the infused ETX stimulate the production rate,

similar to the turnover model shown in Eq 1. As control groups showed no cytokine response,

neither the constant baseline ETX level nor the contamination, described above, contributed

to the stimulation. The best description of tolerance was obtained when the concentration

time-course of ETX–simultaneously to driving TNF-α response–modified the value of EC50,

i.e., EC50 was a function of ETX exposure. This was done through an Emax relationship

(ΔOFV = -122.7 vs. linear), with a delay in the increase of EC50 described by two transit com-

partments (ΔOFV = -894.5 vs. no transits). With this tolerance model, a sigmoidal Emax rela-

tionship between ETX and TNF-α was significant (ΔOFV = -250.1 vs. standard Emax). A large

Table 2. Overview of parameters in the final model, with estimated value, uncertainty, inter-individual variability, and shrinkage.

Parameters (unit) Parameter Description Estimates (RSE%) Variability in CV% (RSE%)c [SHR%]

Vmax (EU/h) Maximum ETX elimination capacity 442000 (1) -

KM (EU/L) Concentration of ETX for half of Vmax 12600 (17) 120 (21) [13]

Vc (L) Volume of distribution for ETX 36.1 (20) 75.3 (25) [24]

BASEETX (EU/L) Baseline ETX (Endochrome, study C+E)b 155 (20) 96.3 (21) [18]

Baseline ETX (Coatest, study F)b 1810 (38)

MIX a (-) Proportion of individuals with contamination 0.399 (20) -

Propcont (-) Proportionality: BASEETX to contamination 132 (15) -

MTTTNF-α (h) Mean transit time for TNF-α in plasma 1.04 (13) 81.5 (28) [14]

S0,TNF-α (ng/L) Baseline TNF-α (DuoSet, study A+B)b 281 (9) 54.1 (23) [13]

Baseline TNF-α (DuoSet, study E)b 25.4 (12)

Baseline TNF-α (BioSource, study C+F)b 3.06 (29)

Baseline TNF-α (BioSource, study D)b 68.2 (15)

Emax (-) Maximum increase of TNF-α production rate 2540 (9) -

EC0 (EU/L) Concentration of ETX at half of Emax,TNF-α 286 (5) -

γ (-) Sigmoidicity coefficient for Emax relationship 2.10 (26) -

MTTEC50 (h) Mean transit time for EC50EC50,TNF-α 6.33 (5) -

Tmax (-) Maximum increase of EC0,TNF-α 45100 (2) -

TC50 (EU/L) Concentration of ETX at half of Tmax 29300 (3) -

MTTIL-6 (h) Mean transit time for IL-6 in plasma 1.45 (11) 47.4 (41) [21]

S0,IL-6 (ng/L) Baseline IL-6 (DuoSet, study A+B+E)b 49.2 (13) 79.9 (10) [6]

Baseline IL-6 (BioSource, study C+D+F)b 8.19 (10)

ESLP,TNF-α (-) Slope for TNF-α increase of Rprod,IL-6 0.961 (9) -

ESLP,ETX (-) Slope for ETX increase of Rprod,IL-6 0.00937 (28) -

σ ETX (%) Proportional error for ETX 32.1 (16) [23]

σ TNF-α (%) Proportional error for TNF-α 48.5 (8) [11]

σ IL-6 (%) Proportional error for IL-6 50.5 (8) [11]

Abbreviations: CV%: coefficient of variation; ETX: endotoxin; EU: endotoxin units; IL-6: interleukin-6; RSE%: relative standard error in percent; SHR%: shrinkage in

percent; TNF-α: tumor necrosis factor alphaa parameter was fixed in final estimation, and the RSE% is from the final run of the ETX modellingb The letters (A-F) refer to the study as designated in Table 1.c Reported on the approximate standard deviation scale (standard error/variance estimate)/2.






variation was observed in the baseline TNF-α (S0,TNF-a) among the included studies, and dif-

ferent baselines were tested on a per-study basis. This resulted in four different typical base-

lines (ΔOFV = -120.5 vs. one shared), varying from 3.06 to 281 ng/L, with higher values for the

DuoSet assay. However, the relative increase in TNF-α at a certain exposure of ETX did not

differ across the studies, as there was no significant differences in Emax.

The model was extended to IL-6 by letting TNF-α stimulate the production of IL-6 through

a linear relationship. As different baseline TNF-α (S0,TNF-a) were used among the studies the

relative increase was used to drive the effect, as in:

EFFTNF� a ¼ ESLP;TNF� a �CTNF� a

S0;TNF� a� 1

!

ð2Þ

where ESLP,TNF-α describes the proportionality between relative increase in TNF-α and stimula-

tion of IL-6 production. To describe the delayed increase in plasma IL-6, four transit compart-

ments were added to the model (ΔOFV = -255.7 vs. no transits). In addition, an effect of the

ETX time-course (linear relationship) on the production of IL-6 was found significant (ΔOFV =

-268). No improvements could be identified with more complex effect models (Emax, sigmoidal

Emax) for either TNF-α or ETX. As for TNF-α, differences in baseline (S0,IL-6) was significant

(ΔOFV = -83.6), with one estimated baseline per assay (8.19 and 49.2 ng/L).

Inclusion of IIV terms were significant for baselines (S0,TNF-a and S0,IL-6) and the first-order

rate constants describing cytokine degradation (kdeg,TNF-α and kdeg,IL-6 in Fig 1). Correlation in

the individual empirical Bayes’ estimates (EBEs) were also assessed (e.g. high S0,TNF-a could

correspond to high S0,IL-6), but no such relations were identified. Lastly, for all three outcomes

the initial additive model on log-transformed data were adequate for description of RUV.

The final model was run with all structural parameters and variances unfixed, except the

parameter describing the mixture proportion for ETX contamination. This parameter was

fixed to the final estimate in the ETX sub-model (0.399, describing a proportion of

Fig 2. Visual predictive checks for endotoxin based on the final model, stratified by study and infusion rate or design (studies C, E & F in Table 1), with

the endotoxin infusion rate indicated for each panel. The red solid lines and circles correspond to the median observed concentration, while the dashed line

correspond to the median simulated concentration. The shaded area between the two solid lines correspond to the 95% confidence interval for the median

simulation.






individuals), because the inclusion of individuals without ETX observations led to instability

in the estimation of this parameter. The final fit was evaluated using prediction corrected

visual predictive checks (VPCs) stratified by study and infusion rate or design (shown in Fig 2

for ETX, Fig 3 for TNF-α and Fig 4 for IL-6). Generally, all panels showed that the medians of

the observations were well predicted by the model for the different infusion rates and designs.

To assess if the included IIV terms were adequate, prediction corrected VPCs were stratified

by study only to compare the observed and simulated outer percentiles, which also confirmed

an acceptable description.

External evaluation

In the held-out data (study G in Table 1) both cytokines were assayed using DuoSet [24],

though all IL-6 baseline values were set to 200 ng/L (employed limit of quantification (LOQ)

in for this data). Because of the varying TNF-α baselines between studies using the DuoSet

assay, and because all baseline measurements of IL-6 were below the LOQ, the median of the

individual EBEs were used as the typical values when simulating from the final model (205 and

49.3 ng/L for TNF-α and IL-6, respectively). All other parameters and variances were set to the

final values reported in Table 1. The VPC shown in Fig 5 demonstrates a good agreement

between the observed median cytokine time-course in the held-out data, and the median and

its confidence interval based on simulations from the final model.

Illustrating model properties

Predictions for a 30 h period were done for infusion rates similar to those in the available data

(63–16000 EU/kg/h, assuming an ETX batch with a potency of 1000 EU/μg), with the lower

Fig 3. Visual predictive checks for tumor necrosis factor alpha based on the final model, stratified by study and infusion rate or design (studies A-F in

Table 1), with the endotoxin infusion rate indicated for each panel. The red solid lines and circles correspond to the median observed concentration, while

the dashed line correspond to the median simulated concentration. The shaded area between the two solid lines correspond to the 95% confidence interval for

the median simulation. The dashed horizontal lines corresponds to the assay lower limit of quantification, with observations below set to half of this limit for

illustration.






rates changed to 4000 EU/kg/h after the first 15 h to illustrate tolerance aspects. The predic-

tions of ETX, TNF-α and IL-6 as well as the dynamical change in EC50 are shown in Fig 6,

with dashed lines indicating extrapolation outside the available data (primarily for high infu-

sion rates). It is observed for model predictions of TNF-α, that initial infusion rates above 250

EU/kg/h limits the possibility to further elicit a response by increasing the infusion rate at a

later time-point. Furthermore, it can be seen for model predictions of IL-6, that the highest

infusion rates leads to consistently elevated IL-6 concentrations in the extrapolated parts, due

Fig 4. Visual predictive checks for interleukin-6 based on the final model, stratified by study and infusion rate or design (studies A-F in Table 1), with

the endotoxin infusion rate indicated for each panel. The red solid lines and circles correspond to the median observed concentration, while the dashed line

correspond to the median simulated concentration. The shaded area between the two solid lines correspond to the 95% confidence interval for the median

simulation. The dashed horizontal lines corresponds to the assay lower limit of quantification, with observations below set to half of this limit for illustration.


Fig 5. Visual predictive checks for observations of (A) tumor necrosis factor alpha and (B) interleukin-6 from an external dataset (study G in Table 1), with

the endotoxin infusion rate indicated for each panel. The red solid lines and circles correspond to the median observed concentration in the external dataset,

while the dashed line correspond to the median simulated concentration based on the final model. The shaded area between the two solid lines correspond to

the 95% confidence interval for the median simulation. The dashed horizontal line in (B) corresponds to the assay lower limit of quantification (200 ng/L), with

observations below set to half of this limit for illustration.










to the constant ETX-associated stimulation becoming increasingly impactful as the infusion

rate increases. This aspect is illustrated in Fig 7 utilizing the same design, where the contribu-

tion of TNF-α to stimulation of IL-6 production is transitory and more-or-less negligible at 15

h for the highest infusion rates, whereas the stimulation by ETX is constant.

Discussion

The presented work is, to our knowledge, the first that provides a non-linear mixed-effects

model-based assessment of the ETX time-course and its effect on the production of two

important cytokines in the innate immune response, TNF-α and IL-6. The developed model is

based on a comprehensive dataset with a wide range of ETX infusion rates, administered over

varying durations and under different designs. The studies were carried out in large mammals,

expected to resemble humans with respect to physiology and immunological properties [25],

which may be key for future extrapolation of the results.

The observed ETX time-course was adequately described (see Fig 2) using a one-compart-

ment model with saturable elimination, in line with observed differences in half-life between

two dose-groups in rhesus monkeys [26]. Further, radioactively labelled ETX are primarily

found in plasma, liver, and spleen, the two latter being part of the reticuloendothelial system

responsible for the (saturable) systemic elimination of ETX [27]. Two-compartmental kinetics

has been reported [26, 28], but the combination of intravenous infusion, hourly sampling, and

lack of elimination phase samples in our data, limited the determination of a more complex

distribution model. The presented model was built on ETX concentration data following a

wide range of infusion rates, unique and valuable in light of the challenges with ETX determi-

nation [29]. Important for this work, a model for the ETX concentration-time course is critical

in terms of exposure-response where, under non-linear kinetics, change in exposure may not

be proportional to the change in infusion rate. Nonetheless, the model would benefit from

addition of ETX samples collected over longer durations than six hours and with more inten-

sive sampling during the elimination phase.

The time-course of TNF-α displayed a rapid increase with peak concentration at the one-

hour sample for most individuals, followed by a return towards baseline levels [30]. With a

clear relationship between ETX infusion rate and peak TNF-α [20], the starting point was to

let the ETX concentration-time course, a surrogate for TLR-4 activation [31], stimulate the

TNF-α production rate. Even though this could describe the peaks, extension of the model was

needed to handle the development of tolerance, implemented by letting the ETX concentra-

tion-time course describe a (delayed) increase in the potency parameter (EC50). The imple-

mentation was possible due to the study design with ETX infusions allowing for the separation

of ETX and TNF-α time-courses. Alternative methods could have relied on anti-inflammatory

mediators [32] to, for instance, negate the stimulation caused by ETX, but these were not avail-

able in the current dataset. In Fig 3A, the implementation of tolerance describes the difference

in TNF-α response following a 4000 EU/kg/h ETX challenge, after two different pre-exposures

of 63 and 250 EU/kg/h. A pronounced response to the challenge is observed following low

pre-exposure, whereas a response is barely seen following the high pre-exposure, with both

responses much lower than without any pre-exposure. The model was also able to describe

Fig 6. Final model predictions of the time-courses of endotoxin (A), tumor necrosis factor alpha (B), interleukin-6

(C), and the potency parameter EC50 (D). Different initial infusion rates of endotoxin, in EU/kg/h, were used: Control

(designated with a light blue line), 63 (blue), 250 (light green), 500 (green), 1000 (pink), 4000 (red), 8000 (yellow), and

16000 (orange), changed to 4000 EU/kg/h after 15 h for the lower rates of 63, 250, 500, and 1000 EU/kg/h, to

demonstrate tolerance aspects. The dashed part of the lines indicate extrapolation beyond the period of the observed

data.






differences observed following a decelerating or accelerating ETX infusion design (Fig 3D),

and while there are signs of slight differences in TNF-α trajectory between studies, the model

provides a good general description of TNF-α across the included data.

The model was extended to IL-6, whose peak plasma concentration is delayed compared to

TNF-α [30]. This was handled by letting the time-course of TNF-α stimulate the production of

IL-6, with addition of transit compartments to delay the increase in the IL-6 plasma concentra-

tion. This is appropriate, as it has been demonstrated that administration of TNF-α, indepen-

dently of ETX, can increase IL-6 [33, 34], and as the tolerance already included for TNF-α will

then be directly reflected in the time-course of IL-6. However, the model was improved when

the time-course of ETX also contribued to the stimulation of IL-6 production, reflecting that

the optimal description of immune system components is multifaceted with many interrelated

stimulations and inhibitions. That both effects on IL-6 production follow a linear relationship

could be because of difficulties in separating the effects under more complex models, because

non-linearity is already captured in the established relation between ETX and TNF-α, or

because the stimulation in the underlying data was not high enough to reach saturation. How-

ever, all fits presented in Fig 4 show that the final model acceptably captures the observed IL-6

time-courses.

The ability of the model to predict the held out study, including an infusion rate of 1500

EU/kg/h that was not available among the studies used for model building, is shown in Fig 5.

The good agreement between the observed data and model predictions demonstrate, that the

model can be extended to predict piglet studies outside the modelled data, an aspect that adds

certainty in prediction of new studies and generalisation of the model. The model structure

suggested might also be useful in predicting studies in other species but would likely require

information on cytokine baselines and any differences in susceptibility to ETX that would

influence the exposure-response relationship established in piglets (likely EC50).

Improved understanding of model behaviour may be gained from the 30 h predictions

shown in Fig 6, illustrating how the modelled outcomes respond across the available ETX infu-

sion rates and how the value of EC50 changes dynamically as a function of ETX exposure. In

addition, Fig 7 shows the increasing contribution of ETX to IL-6 stimulation with higher infu-

sion rates, whereas the contribution from TNF-α and ETX is approximately equal at the lower

infusion rates, with TNF-α responsible for the peak. The high contribution from ETX at the

higher infusion rates cannot be confirmed based on the current data, and as mortality

occurred within the confines of a six-hour period [20], it is doubtful that such data could be

Fig 7. The respective contribution of endotoxin (light green line) and tumor necrosis factor alpha (light blue line)

time-courses on the stimulation of interleukin-6 production. The initial infusion rate of endotoxin is indicated in

each panel description, changed to 4000 EU/kg/h after 15 h for the lower rates of 63, 250, 500, and 1000 EU/kg/h to

demonstrate tolerance aspects.






obtained. As such, it is unclear if the high constant concentrations of IL-6 at infusion rates at

or above 4000 EU/kg/h are realistic, or if it is only an extrapolation of the linear relationship

between ETX and IL-6, valid for the first six hours and lowest infusion rates.

A previous analysis based on similar data linked measurements of cytokines and organ

function based on literature and inferences from a principal component analysis, with adap-

tion of values to data from individual pigs [14]. However, even though the pigs received similar

treatment, large differences in parameters were required to describe differences in observa-

tions. This is in contrast to the model presented here, which simultaneously describes the gen-

eral data tendency (the “typical” piglet) as well as each individual piglet profile (posthoc),

through fixed effects and associated variances.

A recently published analysis [35] utilizing a modelling approach more similar to the one

presented here, relied on a hypothetical unobserved compartment of anti-inflammatory cyto-

kines to model inhibition of TNF-α and IL-1β release. This approach would work similarly to

our dynamic change in EC50 for the acute tolerance, as both approaches ties cytokine inhibi-

tion directly to the pathogen burden. It is likely however, that some modifications would be

needed to describe the lowered cytokine response upon a second ETX expsoure, though the

most ideal scenario in both cases would be the sampling and availability of key anti-inflamma-

tory cytokines or other measures of pro-inflammatory counter-response.

The presented work is the first step in a more comprehensive model-based framework of

immune-system response to a bacterial marker, with potential extension to additional markers

of inflammation, anti-inflammation or organ dysfunction. This could for instance include

immune cells (e.g. neutrophils and lymphocytes) and circulatory or respiratory changes (e.g.

mean pulmonary arterial pressure). The potential of coupling ETX to organ dysfunction is

interesting, as the underlying animal model is expected to have similarities with humans, espe-

cially with regards to circulatory function [25]. A model-based framework could ultimately

inform treatment decisions in the ICU where critical illness, such as sepsis, has a large impact

on physiological processes such as fluid shifts, permeability, cardiac output or kidney function,

underlying the PK–and thus PD–of therapeutic drugs [36, 37]. Further, while the PK behavior

of antibiotics has been studied in both healthy volunteers and patients, the established differ-

ences has, to our knowledge, not been explained by directly linking changes in the underlying

organ function to the changes in the PK of patients.

The work presented here can be applied to and aid in the development of new treatments

within immunology, by informing early animal experiments (ETX dose and administration

design, choice of sampling times, reducing the number of animals). The administration of

purified E. coli ETX allows the TLR-4 induced activation of the immune response to be studied

with a controlled exposure, which is not possible when using live bacteria. However, the estab-

lished relation between ETX, TNF-α and IL-6 could be further extended by incorporating data

on the release of ETX from live bacteria in the context of antibiotic administration [38, 39].

Further, data from the response following administration of living bacteria, either intrave-

nously or as a localized infection, could be incorporated to model how such a cytokine

response differs from the fixed TLR-4 response presented here [40, 41]. This could form the

basis for predictive links between the porcine endotoxemia model and the ETX challenge

model in healthy volunteers [30], where doses are limited and not close to establishing sepsis.

To conclude, the presented work established a non-linear mixed effects model for adminis-

tered ETX and its induction of the two inflammatory cytokines TNF-α and IL-6. The model

can be used as a basis for the understanding immune response to bacterial infection with dif-

ferent bacterial loads and for the simulation of new studies to answer design questions and/or

inform pre-clinical studies.




Materials and methods

Ethics statement

This work relied on previously published data that was generated in studies involving live ani-

mals. Animals were handled according to guidelines of the Swedish National Board for Labo-

ratory Animals and the European Convention on Animal Care, and study designs and

procedures were approved by the Animal Ethics Committee of Uppsala, Sweden (Uppsala

djurforsoksetiska namnd, permit no. 215/5).

Data

The model development was based on data from six pre-clinical in vivo studies carried out by

the same research group and under similar conditions. The studies, including a seventh study

used for external evaluation, are described shortly in Table 1, accompanied by information on

the number of individuals, ETX infusion rates, number of samples, samples below the limit of

quantification (BLOQ), assays and their LOQ, with additional information available in the

respective publications. In total, the analysis was based on 281 ETX samples, 1077 TNF-α sam-

ples (169 BLOQ) and 1053 IL-6 samples (101 BLOQ), from 116 piglets. Prior to analysis, 27 of

the observations (spread across individuals and outcomes) were excluded as outliers (obvious

deviation from the individual concentration-time profiles).

Study design. All studies were performed in anaesthetized piglets with an age of approxi-

mately 12 weeks and a mean weight of approximately 27 kg. Anaesthesia and preparatory pro-

cedures were similar across the studies, with reference to respective publications for additional

information given in Table 1.

The studies used Escherichia coli: 0111:B4 ETX (Sigma Chemical, St. Louis, MO) as an

active agent, though the potency (i.e. endotoxin units (EU) per mass) of batches varied as

shown in Table 1. The ETX was administered as continuous intravenous infusions at rates

adjusted to the individual weight of the piglet, spanning from zero (saline) to 16 μg/kg/h, but

referred to and handled in the model as EU/kg/h. Samples for ETX and cytokines were taken

prior to ETX administration and then hourly to every third hour for the rest of the study dura-

tion. A range of other variables were measured, for example measurements related to organ

dysfunction and physiological state, as well as immune cell-counts and haematology, but this

analysis focused on the cytokines TNF-α and IL-6.

Bioanalytical assay. For ETX, analysis was performed using two different commercial

chromogenic limulous amoebocyte lysate assays without a defined LOQ [42]. For the cyto-

kines, three commercial sandwich enzyme-linked immunosorbent assay kits were used, with

or without a defined LOQ (10 ng/L or 60 ng/L) dependent on the study (see Table 1).

Software

The nonlinear mixed-effects modelling software NONMEM 7.4.2 (ICON Development Solu-

tions, Hanover, MD, US) [43] was used for estimating model parameters, with Perl-speaks-

NONMEM and Piraña used for facilitating model execution and handling the modelling

workflow [44]. NONMEM models were executed on a Scientific Linux 6 computing cluster

running Intel Xeon E5 nodes. R [45] was used for handling of raw data and analysis of NON-

MEM output with packages xpose4 [46], ggplot2 [47] and tidyr [48].

Modelling process

The available data were modelled in a sequential order, initially aiming at describing the distri-

bution and elimination of the infused ETX, its induction of TNF-α shown as a rapid increase




in plasma concentration, and lastly extended to IL-6. With acceptable results for one outcome

all parameters would be fixed in the following step, with the final run leaving all parameters

unfixed for a simultaneous fit [49]. All data were log-transformed and estimated using impor-

tance sampling with interaction. As a large portion of the data, especially baseline cytokine

samples, were BLOQ the likelihood based M3 method [50] was implemented, with the Lapla-

cian method included for this extension.

Evaluation of model fits were based on likelihood-ratio tests of the OFV of two nested mod-

els, the precision of the parameter estimates (relative standard error, RSE%), and the adequacy

of residual goodness-of-fit plots and appropriately stratified simulation-based VPCs [51]. IIV

was included to produce lognormal distributed parameters, and an additive relation was used

for RUV (approximately proportional with log-transformed data).

Infused endotoxin

One- and two-compartment models were tested with either linear or non-linear elimination

pathways. In addition, different approaches were taken to describe the baseline ETX level (or

assay baseline) primarily informed by the samples from the control groups and the pre-dose

measurements, as well as a general tendency of high ETX observations in some individuals

before the infusion of ETX or saline was started (evident across dose groups).

Host response: TNF-α and IL-6

A framework of turnover models were chosen to describe the change in cytokine concentra-

tion, as their parameterization provide parameters that are relatable in a biological context.

Turnover models consist of a zero-order production rate (Rprod), a first-order rate constant

describing degradation (kdeg), and a baseline (S0) given by the ratio Rprod/kdeg. The system can

be disturbed, for instance by stimulating the production rate through an Emax relationship to

the ETX concentration (CETX), as described for TNF-α by:

dCTNF� a

dt¼ Rprod;TNF� a � 1þ

Emax � CETX

EC50 þ CETX

� �

� kdeg;TNF� a � CTNF� a ð3Þ

where Emax describes the maximum effect and EC50 is the potency (CETX for half maximum

effect), with the baseline (S0,TNF-α) given by:

S0;TNF� a ¼Rprod;TNF� a

kdeg;TNF� að4Þ

Extensions of this system were explored, e.g. transit compartments were added to describe

delays and functions describing development of tolerance were explored. Time-dependent

changes in either Emax or EC50 were initially considered, but as reliance on time is not optimal

for predictive capability or for capturing the tolerance dynamics of repeated ETX administra-

tion, models independent of time were desired as a final implementation [52].

External evaluation

Data from a study that was not used in the model building process [24] was available to evalu-

ate the final models’ ability to predict the observed TNF-α and IL-6 time-courses. The external

evaluation was performed by comparing the median of the observations from this separate

study, to simulations from the final model using the design of the external study. The cytokine

baselines were derived from the median of the EBEs for those individuals analysed with the

corresponding assay.




Supporting information

S1 Table. Raw endotoxin and cytokine dataset used in model development. Dataset used in

development of the model, including information on each individuals administration of ETX

and observed ETX, TNF-α and IL-6 concentrations at given times, plus any important infor-

mation of the respective studies with regards to study design or similar.

(CSV)

S1 Text. Final model file including differential equations. Model control file for the final

model, showing input, compartments, parameters, initialization and differential equations,

predictions of observations and observations below the limit of quantification, initial estimates

for parameters and variances and estimation method.

(PDF)

Author Contributions

Conceptualization: Anders Thorsted, Salim Bouchene, Miklos Lipcsey, Mats O. Karlsson,

Lena E. Friberg, Elisabet I. Nielsen.

Data curation: Anders Thorsted.

Formal analysis: Anders Thorsted, Salim Bouchene, Mats O. Karlsson, Lena E. Friberg, Elisa-

bet I. Nielsen.

Funding acquisition: Mats O. Karlsson, Lena E. Friberg, Elisabet I. Nielsen.

Investigation: Eva Tano, Markus Castegren, Miklos Lipcsey, Jan Sjolin.

Resources: Eva Tano, Markus Castegren, Miklos Lipcsey, Jan Sjolin.

Supervision: Mats O. Karlsson, Lena E. Friberg, Elisabet I. Nielsen.

Writing – original draft: Anders Thorsted.

Writing – review & editing: Anders Thorsted, Salim Bouchene, Eva Tano, Markus Castegren,

Miklos Lipcsey, Jan Sjolin, Mats O. Karlsson, Lena E. Friberg, Elisabet I. Nielsen.

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